          Cyclotron | particle energy

Particle energy

Since the particles are accelerated by the voltage many times, the final energy of the particles is not dependent on the accelerating voltage but on the strength of the magnetic field and the diameter of the accelerating chamber, the dees. Cyclotrons can only accelerate particles to speeds much slower than the speed of light, nonrelativistic speeds. For nonrelativistic particles, the centripetal force $F_{C}\;$ required to keep them in their curved path is

$F_{C}={mv^{2} \over r}\;$ where $m\;$ is the particle's mass, $v\;$ its velocity, and $r\,$ is the radius of the path. This force is provided by the Lorentz force $F_{B}\,$ of the magnetic field $B\,$ $F_{B}=qvB\;$ where $q\,$ is the particle's charge. The particles reach their maximum energy at the periphery of the dees, where the radius of their path is $r\;=\;R$ the radius of the dees. Equating these two forces

${mv^{2} \over R}=qvB\;$ $v={qBR \over m}\,$ So the output energy of the particles is

$E={1 \over 2}mv^{2}={\frac {q^{2}B^{2}R^{2}}{2m}}\;$ Therefore, the limit to the cyclotron's output energy for a given type of particle is the strength of the magnetic field $B$ , which is limited to about 2 T for ferromagnetic electromagnets, and the radius of the dees $R$ , which is determined by the diameter of the magnet's pole pieces. So very large magnets were constructed for cyclotrons, culminating in Lawrence's 1946 synchrocyclotron, which had pole pieces 4.67 m (184 in) (15.3 feet) in diameter.

Other Languages
Afrikaans: Siklotron
العربية: مسرع دوراني
azərbaycanca: Siklotron
беларуская: Цыклатрон
български: Циклотрон
català: Ciclotró
čeština: Cyklotron
dansk: Cyklotron
Deutsch: Zyklotron
Ελληνικά: Κύκλοτρο
español: Ciclotrón
Esperanto: Ciklotrono
euskara: Ziklotroi
français: Cyclotron
Gaeilge: Cioglatrón
հայերեն: Ցիկլատրոն
hrvatski: Ciklotron
Bahasa Indonesia: Siklotron
italiano: Ciclotrone
עברית: ציקלוטרון
Jawa: Siklotron
қазақша: Циклотрон
Кыргызча: Циклотрон
magyar: Ciklotron
македонски: Циклотрон
မြန်မာဘာသာ: ဆိုင်ကလိုထရွန်
Nederlands: Cyclotron
norsk: Syklotron
norsk nynorsk: Syklotron
polski: Cyklotron
português: Cíclotron
română: Ciclotron
русский: Циклотрон
Scots: Cyclotron
Simple English: Cyclotron
slovenčina: Cyklotrón
српски / srpski: Циклотрон
srpskohrvatski / српскохрватски: Ciklotron
suomi: Syklotroni
svenska: Cyklotron
Türkçe: Siklotron
українська: Циклотрон
اردو: مداریہ
Tiếng Việt: Máy xiclotron  